Today we will investigate the volume of cubes. DESCRIPTION OF A CUBE  WHAT IS A CUBE?

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Presentation transcript:

Today we will investigate the volume of cubes

DESCRIPTION OF A CUBE  WHAT IS A CUBE?

DESCRIPTION OF A CUBE  A cube is a three-dimensional geometric figure with all sides made of squares called faces.  How many faces does a cube have?

DESCRIPTION OF A CUBE  IT HAS 6 FACES

DESCRIPTION OF A CUBE  Two faces intersect in a segment called an edge.  How many edges does a cube have?

DESCRIPTION OF A CUBE  IT HAS 12 EDGES. length height width

DESCRIPTION OF A CUBE  Three faces intersect in a point called a vertex.  How many vertices does a cube have?

DESCRIPTION OF A CUBE  IT HAS 8 VERTICES

BUILDING CUBES  Complete the cube table using a single cube.  Surface area is the sum of the areas of all the faces.  Volume is the number of cubes needed for the figure – or how many cubes will fit inside the shape.

BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume1x1x1 1 4 units 1 square units 6 square units 1 cubic units Compare your answer.

BUILDING CUBES  Use the snap cubes to build the next larger cube.  What is the size of the cube?

BUILDING CUBES  The size of the cube is 2 x 2 x 2 or 2 units length x 2 units width x 2 units height.  Complete the cube table for this single cube.

 How do your answers compare with these? BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume2x2x2 2 8 units 4 square units 24 square units 8 cubic units

BUILDING CUBES  Look at your answers for the 1x1x1 cube and the 2x2x2 cube. Do you notice any patterns on the table?  Now build the next larger cube.  How large is the cube?

BUILDING CUBES  Size of the cube is 3x3x3.  Complete the table for this cube

 How do your answers compare with these?  Do your patterns still work? BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume3x3x33 12 units 9 square units 54 square units 27 cubic units

BUILDING CUBES  Use the snap cubes to build the next larger cube.  How large is the cube? ANSWER

 Size of cube is 4x4x4. BUILDING CUBES  Complete the cube table for this cube.

 How do your answers compare with these?  Do your patterns still work? BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume4x4x44 16 units 16 square units 96 square units 64 cubic units

 Use your pattern to complete the table for a 5x5x5 cube. BUILDING CUBES

 Now build the cube to see if your patterns work. BUILDING CUBES

Here is the 5x5x5 cube.

BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume5x5x units 25 square units 25 square units 150 square units 150 square units 125 cubic units Compare your answer.

 Use your patterns to complete the table for these cubes. 6x6x67x7x7 6x6x67x7x7 8x8x89x9x9 8x8x89x9x9 10x10x10 10x10x10 BUILDING CUBES ANSWER

BUILDING CUBES Size Edge Length Face Area of 1 Face Surface Area Volume6x6x66 24 units 36 square units 216 sq units 216 cubic units 7x7x77 28 units 49 sq units 294 sq units 343 cubic units 8x8x88 32 units 64 sq units 384 sq units 512 cubic units 9x9x99 36 units 81 sq units 484 sq units 729 cubic units 10x10x units 100 sq units 600 sq units 1000 cubic units

BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume15x15x units 225 square units 225 square units 1350 square units 1350 square units 3375 cubic units Compare your answer.